Given a Binary Tree, the task is to find the size of largest Perfect sub-tree in the given Binary Tree.
Perfect Binary Tree – A Binary tree is Perfect Binary Tree in which all internal nodes have two children and all leaves are at the same level.
Input: 1 / \ 2 3 / \ / 4 5 6 Output: Size : 3 Inorder Traversal : 4 2 5 The following sub-tree is the maximum size Perfect sub-tree 2 / \ 4 5 Input: 50 / \ 30 60 / \ / \ 5 20 45 70 / \ / \ 10 85 65 80 Output: Size : 7 Inorder Traversal : 10 45 85 60 65 70 80
Approach: Simply traverse the tree in bottom up manner. Then on coming up in recursion from child to parent, we can pass information about sub-trees to the parent. The passed information can be used by the parent to do Prefect Tree test (for parent node) only in constant time. A left sub-tree need to tell the parent whether it is a Perfect Binary Tree or not and also need to pass max height of the Perfect Binary Tree coming from left child. Similarly, the right sub-tree also needs to pass max height of Prefect Binary Tree coming from right child.
The sub-trees need to pass the following information up the tree for finding the largest Perfect sub-tree so that we can compare the maximum height with the parent’s data to check the Perfect Binary Tree property.
- There is a bool variable to check whether the left child or the right child sub-tree is Perfect or not.
- From left and right child calls in recursion we find out if parent sub-tree if Prefect or not by following 2 cases:
- If both left child and right child are perfect binary tree and have same heights then parent is also a Perfect Binary Tree with height plus one of its child.
- If the above case is not true then parent cannot be perfect binary tree and simply returns max size Perfect Binary Tree coming from left or right sub-tree by comparing their heights.
Below is the implementation of the above approach:
Size : 3 Inorder Traversal : 4 2 5
- Find the largest BST subtree in a given Binary Tree | Set 1
- Find the largest Complete Subtree in a given Binary Tree
- Find largest subtree sum in a tree
- Find sum of all nodes of the given perfect binary tree
- Queries to find the maximum Xor value between X and the nodes of a given level of a perfect binary tree
- Subtree with given sum in a Binary Tree
- Check if a binary tree is subtree of another binary tree | Set 1
- Check if a binary tree is subtree of another binary tree | Set 2
- Check if the given Binary Tree have a Subtree with equal no of 1's and 0's
- Find largest subtree having identical left and right subtrees
- Convert a Binary Tree such that every node stores the sum of all nodes in its right subtree
- Change a Binary Tree so that every node stores sum of all nodes in left subtree
- Find the Kth node in the DFS traversal of a given subtree in a Tree
- Check whether a given binary tree is perfect or not
- Reverse alternate levels of a perfect binary tree
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : tyagikartik4282